Melting point is the temperature that a solid will change phase into a liquid. In theory it will also be the same temperature as the freezing point, where a liquid will turn into a solid, but in practice there are slight differences. For example, in theory pure water has a melting point and freezing point at 0°C under standard temperature and pressure, but slight measurable differences tend to arise.
While the solid is in the process is melting, its temperature will not change. This is known as latent heat, which is the opposite of sensible heat. The transition between the solid and the liquid is so sharp for small samples of a pure substance that melting points can be measured to 0.1°C. Therefore melting points can be used to accurately measure the purity of a substance.